Digits, Grade 7, Volume 1, Homework Helper

### 7-3: TEKS Practice

• 1. The equation y equals , 5 sevenths , x describes a proportional relationship between x and y. What is the constant of proportionality?

• 2. The equation P = 3s represents the perimeter P of an equilateral triangle with side length s. What is the perimeter of an equilateral triangle with side length 4 ft?

• 3. You bike 11.2 miles in 1.4 hours at a steady rate. What equation represents the proportional relationship between the x hours you bike and the distance y in miles that you travel?

• 4. Marco needs to buy some cat food. At the nearest store, 3 bags of cat food cost \$15.75. How much would Marco spend on 5 bags of cat food?

• 5. An arts and crafts store sells sheets of stickers. Use the table to write an equation you can use to find the total cost y in dollars for x sheets of stickers. • 6. Jane likes to exercise daily. The table shows the number of calories y she burns by exercising steadily for x minutes. How many calories would she burn by exercising for 29 minutes? • 7. Solve the proportion 22 over 24 , equals , t over 84

• 8. In a certain chemical, the ratio of zinc to copper is 3 to 16. A jar of the chemical contains 320 grams of copper. How many grams of zinc does it contain?

• 9. Mental Math Professional chefs usually measure ingredients by weight rather than by volume. A recipe calls for 2 ounces of flour for every 3 ounces of sugar.

• a. If you are a chef and you use 12 ounces of sugar, how many ounces of flour should you use?

• b. Explain how you can use mental math to find the answer. Explain why a chef might need mental math to find an answer like this.

• 10. Writing Ann's car can go 228 miles on 6 gallons of gas. During a drive last weekend, Ann used 7 gallons of gas.

• a. How far did she drive?

• b. Explain how the problem changes if you were given the distance Ann drove last weekend instead of how much gas she used.

• 11. Reasoning The equation y = 6.41x describes a proportional relationship between x and y.

• a. What is the constant of proportionality?

• b. Explain why your answer is called the “constant of proportionality.”

• 12. Multiple Representations The proportions eh over b , equals , c over d and b over eh , equals , d over c are called equivalent proportions.

• a. Find a proportion equivalent to 3 sevenths , equals , 9 over x , .

• A. 7 thirds , equals , 9 over x

• B. 7 thirds , equals , x over 9

• C. 7 ninths , equals , x over 3

• D. 7 over x , equals , 9 thirds

• b. What is the solution of the proportion?

• c. Explain why, based on this example, solving an equivalent proportion can be useful.

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